From Newton to Mandelbrot : A Primer in Theoretical Physics with Fractals for the Macintosh (R)

Nature is full of spidery patterns: lightning bolts, coastlines, nerve cells, termite tunnels, bacteria cultures, root systems, forest fires, soil cracking, river deltas, galactic distributions, mountain ranges, tidal patterns, cloud shapes, sequencing of nucleotides in DNA, cauliflower, broccoli, lungs, kidneys, the scraggly nerve cells that carry signals to and from your brain, the branching arteries and veins that make up your circulatory system. These and other similar patterns in nature are called natural fractals or random fractals. This chapter contains activities that describe random fractals. There are two kinds of fractals: mathematical fractals and natural (or random) fractals. A mathematical fractal can be described by a mathematical formula. Given this formula, the resulting structure is always identically the same (though it may be colored in different ways). In contrast, natural fractals never repeat themselves; each one is unique, different from all others. This is because these processes are frequently equivalent to coin-flipping, plus a few simple rules. Nature is full of random fractals. In this book you will explore a few of the many random fractals in Nature. Branching, scraggly nerve cells are important to life (one of the patterns on the preceding pages). We cannot live without them. How do we describe a nerve cell? How do we classify different nerve cells? Each individual nerve cell is special, unique, different from every other nerve cell. And yet our eye sees that nerve cells are similar to one another. This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, presenting all the central concepts and equations at an accessible level. Chapters 1 to 4 contain the standard material of courses in theoretical physics and are supposed to accompany lectures at the university; thus they are rather condensed. They are supposed to fill one year of teaching. Chapters 5 and 6, in contrast, are written less condensed since this material may not be part of standard lectures and thus could be studied without the help of a university teacher. An appendix on elementary particles lies somewhere in between: It could be a summary of a much more detailed course, or studied without such a course. Illustrations and numerous problems round off this unusual textbook. It will ideally accompany the students all along their course in theoretical physics and prove indispensable in preparing and revising the exams. It is also suited as a reference for teachers or scientists from other disciplines who are interested in the topic. From Newton to Mandelbrot. A Primer in Theoretical Physics with Fractals for the Macintosh ( ) takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a Macintosh diskette where a selection of executable programs exploring the fractal concept can be found. The Diskette The program FRACTAL DIMENSION can be used on any 68030-, 68040,- or PowerPC-based Macintosh with 4 Mb RAM and 256 color display running System 6.7 - 7.5 - Sierpinski gasket - Random walk - Self-avoiding walk - Percolation - Diffusion-limited aggregation (DLA) - Neuron shape From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful colour illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will prove indispensable in preparing and revising for exams. Intended for use in one-year courses in theoretical physics, this book aims to guide students through areas such as classical mechanics, relativity, electrodynamics and the physics of fractals. The text includes computer programs, tests and illustrations to encourage further study of the subject.